I am teaching my first non-examinable graduate course this Winter term. This course is for students ranging from Masters' students to PhD students in Pure Mathematics and is a course for students to see a topic that is a bit more specialised than the typical qualifier type course.
Since it is a bit more specialised, I am having a bit of an issue figuring out where to start. I can start with a bit of background at the risk of boring some of the more advanced PhD students working in my field, or I can tell the students that are not as adept where to find that material to catch up. I am leaning more towards the latter so that I can have more students taking the course, but the course is only 16 one-hour lectures and I want to get to some interesting material that can help someone starting to work in this field. I am also concerned I might be being overzealous in what I can accomplish in this time and might speed right through details that would be useful. (My imposter syndrome is acting up and making me feel like a lot of this stuff is trivial when maybe it's not!)
The question is this: How do you in a topics course balance giving general theory and also the more specific information that is relevant to the current research trend? I'm afraid if I spend too much time on general theory, I may end up not touching on what research is being done today. Would this be bad just spending the last lecture or two in a topics class just punting the question "What's happening nowadays in this field?"
Thanks in advance!